How to make a particle system fade out in transparency?
Not sure if this is best/cleanest way to do it but here is what I figured out. 

I made a hair particle system on a sphere that uses smaller spheres (the stars) as objects to imitate the look of stars like in your render. Then I made this node setup (pictured below) for the material of the star that uses the mapping of the sphere that is holding the particle system to affect a color ramp. That then controls the factor of a mix shader that fades between a transparency and emission shader.



Hope that helps!